Gemara

(Beraisa): If a drop of blood is found, we discard the blood and the egg is permitted.

(R. Yirmeyah): This is only if the blood is found on the knot.

(Dostoy, father of R. Aftoriki - Beraisa): This is only if the blood is found on the white. If it is found on the yolk, the entire egg is forbidden.

This is because the blood spread throughout the egg.

(Rav Gavihah): This Beraisa was said in front of Abaye, but reversed (the law of blood found on the white and yolk). Abaye corrected it.

Kerisus 21a (Beraisa): The Lav against eating blood does not apply to eggs, for they are not meat. It does not apply to fish and grasshoppers, for they are totally permitted.

Rishonim

Rif (22a): If a drop of blood is found, the blood is discarded and the egg is permitted. This is only if the blood is found on the (knot) [white]. If it is found on the yolk, the entire egg is forbidden, because the blood spread throughout the egg.

Rambam (Hilchos Ma'achalos Asuros 3:9): If a drop of blood was found in an egg, if it is on the white, we discard the blood and eat the rest. If it is found on the yolk, the entire egg is forbidden.

Rosh (3:63): Rashi says that if the blood spread past the knot, it forbids everything. Blood found 'on the yolk' means on the knot of the yolk. Surely, it spread from the knot to the white. Even if it spreading is not evident from the knot the white, since it is found on the knot of the yolk, which is opposite the knot of the white, surely it spread from the knot of the white, which is where the chick begins to form. If it is found on the yolk not on the knot, and spreading is not evident from the knot of the white, the egg is permitted. R. Yirmeyah and R. Dostoy do not argue. R. Yirmeyah distinguishes within the white. On the knot, the blood is forbidden and the egg is permitted. If it spread out from the knot, even the egg is forbidden. The same applies if blood is found on the white, or on the yolk that did not come from the knot of the white. (Only) the blood is forbidden. R. Yirmeyah and R. Dostoy discuss only the rest of the egg. The blood is forbidden in every case. R. Dostoy teaches that on the knot of the yolk is like when it spread from the knot of the white.

Rosh (ibid.): Rashi explains like this. This is difficult, for in Kerisus it says that the Lav of blood does not apply to eggs, for they are not meat. It does not apply to fish and grasshoppers, for they are totally permitted. I.e. just like we permit blood of fish and grasshoppers as long as it is on them and it is evident that it came from them, the same applies to blood of eggs. We can say that mid'Rabanan, Chachamim decreed about blood of eggs, due to blood of birds, from which eggs come. The Torah permits even the blood from which the chick forms, i.e. on the knot, even though it would have become a chick in the end. Now, it is not meat, for there is no flesh. Chachamim forbade whether it is on the knot or off the knot. Alternatively, the Torah forbids blood on the knot. It is considered meat, since the chick forms from it. In Kerisus we permit when the blood is not on the knot, rather, elsewhere. Often blood is found right after the egg was laid. (Surely the chick did not yet start to form!) That blood does not come to form a chick. R. Yirmeyah teaches that 'he discards the blood' is when it is found on the knot. Then, the Torah forbids it. What is not on the knot is permitted even mid'Rabanan.

Rosh (ibid.): Rashi totally forbids when it is outside the knot. This is when there is blood on the knot, and it spread from there. According to this, if blood is found on the knot of the white, the Torah forbids it and permits the egg. If it spread outside from the knot of the white, or it is found on the knot of the yolk, it is totally forbidden. If it is found on the white or on the yolk, not on the knot, the first answer forbids the blood mid'Rabanan. The second answer permits it.

Rosh: The Rif did not mention the knot. (The primary version of the text of the Rif says only white - PF.) I.e. we discard the blood and eat the rest if the blood is found on the white. If it is found on the yolk, it is totally forbidden. He always forbids the blood. R. Dostoy distinguishes only between the white and the yolk. Anywhere on the white, the blood is forbidden and the egg is permitted. Anywhere on the yolk, it is totally forbidden. It is good to be stringent to forbid when it spread from the knot, like Rashi, and when it is anywhere on the yolk, like the Rif.

Ran (21b DH Aval, citing the Ro'oh): We cannot be more stringent about the yolk than the white. Chicks form from the white. If you break an egg while the chick is inside, you will not see the white, for it forms from the white, but the yolk is totally intact. Often, freshly laid eggs have blood in the yolk, but not in the white until several days later, when there is concern for chick formation. This is why Rav Ashi told Rav Gaviha that the Beraisa was said oppositely in front of Abaye, and Abaye reversed it. I.e. the initial text was correct. Our version of the Beraisa, based on Abaye, is wrong. We hold like Rav Ashi.

Rebuttal (Gra YD 66:7 LIkut): It is difficult to say that we reject Abaye and the version of the Beraisa in the Gemara. Tosfos (64b DH v'Hu) brings that the Yerushalmi is like Abaye (and the Bavli's version of the Beraisa).

Ran (22a ibid.): R. Yirmeyah taught that if the blood is on the knot and did not spread, the blood is forbidden and the rest is permitted. If it is found on the knot and outside, the entire egg is forbidden, lest it totally spread. He did not explain which knot, so R. Dostai explained that this is only if it is on the knot of the white. If it is found on the knot the yolk, the entire egg is forbidden. If it is found on the white or yolk, not on the knot, there is no concern for formation (of a chick), since it begins to form from the knot. This is blood of eggs, which we permit in Kerisus. However, perhaps that is mid'Oraisa, but mid'Rabanan it is forbidden due to Mar'is Ayin (lest onlookers think that he transgresses), like we decree about blood on a loaf.

Poskim

Shulchan Aruch (YD 66:3): If a drop of blood was found in an egg, we discard the blood and eat the rest. This is if it is on the white. If it is found on the yolk, the entire egg is forbidden.

Rema: Some say that if it is found on the knot of the white and also outside, i.e. it spread from the knot, the entire egg is forbidden. Some are more stringent, and forbid whenever it is on the knot of the white, even if it did not spread at all. From this spread the custom to forbid any egg with blood, whether it is on the yolk or white. Where the custom is to be lenient and discard the blood and permit the egg, when it is permitted one must remove and discard Kedei Kelipah (a peel) with the blood.

Beis Yosef (DH v'Im): The knot is the pointy end of the egg. Rashi explains that the knot is the rooster's semen tied at the pointy end of the egg. The chick forms from there. Since it is still there, it did not spread to the rest. Therefore, one may eat the rest. If it is found on the yolk, the entire egg is forbidden, for it totally spread. The Rosh, Rashba and Ran agreed that according to Rashi, we say that the blood totally spread only when it is found on the knot of the yolk, even if it did not spread from there. If it is found not on the knot, on the white or the yolk, the egg is permitted. Similarly, if it is found on the knot of the white and did not spread, the egg is permitted. The Tur teaches that if we know that the chick started forming, one is liable for the blood.

Beis Yosef (ibid.): Hagahos Maimoniyos (3:9) brings from Sefer ha'Terumah that if we are unsure where the blood was, it is a Safek mid'Rabanan and we are lenient. Sha'arei Dura says that if blood was found on the yolk after it was cooked, and one cannot discern the place of the knot, it is permitted, even though perhaps part was on the knot. We are lenient about a Safek mid'Rabanan. We judge based on how we see it now. We learn from there to every Safek about blood in eggs. However, the Rosh wrote in a Teshuvah that we are stringent. The Tur holds that the Torah forbids some blood of eggs, so none is totally permitted. The Rashba (1:46) says that blood of eggs is forbidden only when it is intact, due to Mar'is Ayin. It does not forbid a mixture. This is only if a chick did not start to form. If it started to form, the Torah forbids the blood. It is not blood of eggs, rather, blood of meat. We are not experts (to know when a chick started forming), so for us, everything is a Safek.

Taz (2): The Rema is like Rashi. The Rif and Rambam hold that R. Dostai argues with R. Yirmeyah, and does not distinguish between the knot and the rest. Anywhere on the yolk is forbidden. Anywhere on the white, the blood is forbidden and the rest is permitted. The Mechaber rules like them. The Rosh and Tur say that one should be stringent for both opinions. In Toras ha'Chatas, the Rema explains that our custom is to totally forbid the egg, for we are not expert regarding what is the knot. There is another reason to forbid. The Ro'oh is more stringent about the white (and forbids if blood is anywhere on the white). The Maharshal says that we hold like the Ro'oh.

Shach (8): The Rema (Toras Chatas) said that nowadays we are not experts to know where is the round part and the pointy part, so we forbid wherever the blood is. The Bach and Divrei Chamudos (342) rejected this, for everyone knows this. Clearly, blood on the sides is far from the knot! Rather, we are concerned for the Ro'oh. Also the Yerushalmi and old texts of the Bavli are more stringent about the white than about the yolk. The Maharshal says that letter of the law we are stringent when it is on the white. When it is on the yolk, we cannot be lenient against the Ge'onim.

Aruch ha'Shulchan (16): The Rashba says that if the egg was Safna d'Ara (not fertilized by a rooster), one may discard the blood and eat the egg.

Igros Moshe (YD 1:36): Nowadays, most eggs are Safna d'Ara. The vast majority of people do not consider [loss of] an egg to be a loss at all. We find that [the Poskim] were stringent about all opinions about eggs, even for mid'Rabanan laws, when we should have been stringent. We do not find this regarding other Isurim, even for Isurei Torah. Since there is a minority of eggs due to roosters, in which the blood forbids the entire egg, it is proper for one who finds blood in an egg to be stringent [and forbid the entire egg]. This is not letter of the law.